Errors in the spectral analysis of long-period seismic body waves

Recent theories of earthquake radiation differ in their predictions as to the behavior of the long-period part of the spectrum, of radiated waves. A numerical model study shows that it is difficult experimentally to distinguish between these theories because of a fundamental difficulty in windowing seismic arrivals that consist essentially of a single cycle (as is often the case for long-period body waves). The effect of noise in the record and of truncation due to later arrivals is to produce spuriously large amplitudes for the long-period part of the spectrum. These errors are amplified if corrections must be made for low instrumental magnifications at these periods. Analyses of records of many earthquakes (four examples are presented) by various techniques show that the radiated body waves have a displacement amplitude spectrum characterized by the existence of a dominant period. This disagrees with theories that predict that long periods have a constant amplitude, and thus studies of the long-period spectrum interpreted in terms of these theories may yield results that are grossly in error. Our experimental results are in agreement with Archambeau's theory, which predicts the existence of a dominant period.